Is (cos(2x)-cos(4x))/(sin(2x)+sin(4x))=tan(x) ?

The answer to whether (cos(2x)-cos(4x))/(sin(2x)+sin(4x))=tan(x) is True

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prove (cos(2x)-cos(4x))/(sin(2x)+sin(4x))=tan(x)

prove

\frac{cos ( 2 x ) - cos ( 4 x )}{sin ( 2 x ) + sin ( 4 x )} = tan (x)

True

Solution steps

\frac{cos ( 2 x ) - cos ( 4 x )}{sin ( 2 x ) + sin ( 4 x )} = tan (x)

Manipulating left side

\frac{cos ( 2 x ) - cos ( 4 x )}{sin ( 2 x ) + sin ( 4 x )}

Rewrite using trig identities

= \frac{sin ( x )}{cos ( x )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

sec (\frac{7 π}{4})

sin (- \frac{11 π}{12})

arcsin (0)

arccos (- \frac{3}{2})

tanh (0)

Is (cos(2x)-cos(4x))/(sin(2x)+sin(4x))=tan(x) ?
The answer to whether (cos(2x)-cos(4x))/(sin(2x)+sin(4x))=tan(x) is True